Exchange interactions in ɛ-Fe₂O₃: GGA + U calculations

We have studied the origin of magnetic interaction in ɛ-Fe₂O₃ by ab-initio electronic structure calculations. The exchange integrals of the Heisenberg Hamiltonian have been calculated using the methods based on the density functional theory (DFT) employing generalized gradient approximation (GGA) with orbital dependent potential extension for 3d electrons of Fe (GGA + U method). The calculations confirm the ground antiferromagnetic (AFM) state with two Fe³⁺ sublattices oriented up (Fe2 and Fe3) and two Fe³⁺ sublattices oriented down (Fe1 and Fe4). The calculated exchange integrals, including also the intra-sublattice ones, are all of AFM type. Their strength weighted by the number of neighbors is larger between the Fe sublattices with opposite spins than between the sublattices with equal spin directions. The notable exception is a strong exchange integral between the neighboring tetrahedrally-coordinated sites within the Fe4 sublattice, which effectively decreases the molecular field imposed on Fe4 sites by neighboring sites of other sublattices, namely the antiparallelly oriented Fe2 and Fe3. For this reason, the ordered magnetic moment of Fe4 exhibits the fastest decrease with increasing temperature among the sublattices, leading to an uncompensated AFM arrangement in ɛ-Fe₂O₃. Considering the competition of the inter- and intra-sublattice exchange integrals and applying symmetry arguments, we infer that the collinear AFM ground state of ɛ-Fe₂O₃ is prone to an intrinsic canting within the sublattices, retaining at the same time the magnetic group symmetry Pna'2₁'.